In the framework of a continuum theory, it is shown that the direct bulk flexoelectric response of a finite sample essentially depends on the surface polarization energy, even in the thermodynamic limit where the body size tends to infinity. It is found that a modification of the surface energy can lead to a change in the polarization response by a factor of two. The origin of the effect is an electric field produced by surface dipoles induced by the strain gradient. The unexpected sensitivity of the polarization response to the surface energy in the thermodynamic limit is conditioned by the fact that the moments of the surface dipoles may scale as the body size. (C) 2016 AIP Publishing LLC.